Boxes not colliding with each other
From the information given, it seems you are trying to use dynamic rigid bodies with keyframes, but haven't set them up to allow the animation system to take over the simulation. There is a difference between the two setups, so I will leave a basic example of of how this can be done:

First the difference between the two:

Dynamic rigid bodies-

strictly controlled by physics:



Animated rigid bodies-

controlled by the animation system until you change this!:



Here's how to set it up:

1. Add a rigid body simulation. Active, and dynamic, and select
    animated. Also, use the collision margin, and set this fairly high. The limit is 1. Do this for both objects. You can also play with the mass options if you like. Also, apply transforms with Ctrl+A>rotation &amp; scale



2. Insert a location keyframe at frame 1 for each object with I>location.

3. Select and add a keyframe to the animated checkbox in the physics panel at the same
    frame the simulation will begin by hovering over the checkbox and pressing I.

4. Set your end keyframe for the collision of your objects, and again choose location, or what whatever is applicable to your needs.

5. At the frame following the collsion uncheck the animated
    option in the rigid body options for each object, and set a new
    keyframe.

From this you should be able to expand and make many interesting simulations from colliding cubes to anything else.